DETERMINATION AND ANALYSIS OF ELECTRODYNAMIC FORCES IN A CONDUCTIVE WAVEGUIDE DURING THE PROPAGATION OF AN AMPLITUDE-MODULATED RADIO PULSE
DOI:
https://doi.org/10.32782/mathematical-modelling/2022-5-2-6Keywords:
circular waveguide, radio pulse, magnetic field strength, ponderomotive force, electrodynamic forcesAbstract
A physico-mathematical model for determining the axial component of the magnetic field intensity vector in an electrically conductive circular waveguide when an amplitude-modulated radio pulse propagates in it is proposed. An electrically conductive circular waveguide is modeled by a two-layer hollow cylinder. The outer steel layer is the base, and the inner copper layer is a thin coating. The action of the considered radio pulse is given by the values of the axial component of the magnetic field intensity vector on the inner and outer surfaces of the waveguide. During the propagation of a radio pulse in the waveguide, ponderomotive forces arise, which determine the distribution of electrodynamic forces along the cross-section of the waveguide. Maxwell's relations of electrodynamics were chosen as the initial system of equations, on the basis of which a planar axisymmetric problem of electrodynamics for a long double-layer conductive hollow cylinder was formulated. To construct the solution of the formulated initial-boundary problem of electrodynamics, the approximation of the axial component of the magnetic field intensity vector by the radial variable by a quadratic polynomial in each constituent layer of the waveguide was used. The polynomials approximating the defining function in each component layer of the waveguide are chosen in such a way as to take into account the given boundary conditions on the defining function, both on the inner and outer surfaces of the waveguide, and on the surface of the base-cover connection. This made it possible to reduce the original initial-boundary value problem on the determining function to the corresponding Cauchy problem on the integral characteristics of this function in the radial variable. The general solutions of the Cauchy problem for homogeneous nonstationary electromagnetic action, as well as for homogeneous propagation of a radio pulse in a waveguide, are recorded. The expression of the ponderomotive force in the waveguide during the propagation of a radio pulse in it is obtained. To analyze the electrodynamic forces in the waveguide during the propagation of the radio pulse, the change in the ponderomotive force over time and its distribution over the thickness of the waveguide wall depending on the amplitudefrequency characteristics of the radio pulse were numerically analyzed.
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